Abstract

In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster–Tarski theorem has also been established using our results.

Highlights

  • At present, fixed point theory is an immensely active area of research due to its applications in multiple fields

  • In the present paper, we prove some fixed point theorems in the case of set valued mappings in the setting of a metric space with a graph by defining a new notion called start point of a directed graph

  • It is easy to see that T is a self path map but G has no fixed point and no start point either

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Summary

Introduction

At present, fixed point theory is an immensely active area of research due to its applications in multiple fields. Investigated the fixed point results in nonlinear contraction mappings. Nadler [19] and Assad and Kirk [20] established some very important fixed point results for set valued and multivalued contraction mappings.

Results
Conclusion

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